The 6-foot-5 (1.96-meter) Gerasimov, 26, saved both break points against him and converted his only one against the 6-foot-4 (1.93-meter) Kokkinakis, 23.
Gerasimov reached two quarterfinals on the ATP Tour, in Los Cabos and Moscow, last year. He defeated three top-60 players in the process, including then-No. 28 Sam Querrey in Los Cabos.
Kokkinakis, whose promising career has been derailed by injuries, shocked Roger Federer in the second round in Miami in March 2018. He is ranked No. 171 after climbing as high as No. 69 at 19 years old in 2015.
Gerasimov, ranked No. 146, is scheduled to face 12th-seeded Emilio Gomez, an Ecuadorian ranked No. 169, on Thursday for a quarterfinal berth. They will meet for the first time.
Top-seeded Damir Dzumhur of Bosnia and Herzegovina beat Keegan Smith, a 6-foot-7 (2.01-meter) qualifier from San Diego, 6-4, 6-4. Smith won the NCAA doubles title as a UCLA sophomore with Maxime Cressy last May in Orlando, Fla.
The 5-foot-9 (1.75-meter) Dzumhur, who has plunged from a career-high No. 23 last July to No. 109, will meet unseeded Lukas Lacko of Slovakia.
The 31-year-old Lacko, down from a career-high No. 44 in 2013 to No. 227, topped 6-foot-7 American Christopher Eubanks, an Aptos semifinalist last year, 7-6 (1), 7-6 (5).
Dzumhur and Lacko have split two career matches.
Fifth-seeded Bjorn Fratangelo of Orlando beat Italy's Jannik Sinner, who won last week's $54,160 tournament in Lexington, Ky., 7-6 (6), 6-3. Fratangelo won the $100,000 Fairfield (Calif.) Challenger last October and reached the Aptos semifinals in 2015 and 2016.
Second-seeded Steve Johnson of Redondo Beach in the Los Angeles area dismissed Roberto Quiroz of Ecuador 6-1, 6-2 in 48 minutes. Johnson, the 2012 Aptos champion, has tumbled from a career-high No. 21 in 2016 to No. 93.
Johnson will meet unseeded Liam Broady, a left-hander from Great Britain. Broady, the 2017 Aptos runner-up, beat 14th-seeded Ramkumar Ramanathan of India 7-6 (2), 6-4.
Here are the updated Aptos singles and doubles draws and Thursday's schedule. Live streaming is available.
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